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%TCIDATA{Created=Thursday, May 13, 2004 12:57:43}
%TCIDATA{LastRevised=Wednesday, June 11, 2008 15:12:36}
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\newtheorem{theorem}{Theorem}
\newtheorem{acknowledgement}[theorem]{Acknowledgement}
\newtheorem{algorithm}[theorem]{Algorithm}
\newtheorem{axiom}[theorem]{Axiom}
\newtheorem{case}[theorem]{Case}
\newtheorem{claim}[theorem]{Claim}
\newtheorem{conclusion}[theorem]{Conclusion}
\newtheorem{condition}[theorem]{Condition}
\newtheorem{conjecture}[theorem]{Conjecture}
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{criterion}[theorem]{Criterion}
\newtheorem{definition}[theorem]{Definition}
\newtheorem{example}[theorem]{Example}
\newtheorem{exercise}[theorem]{Exercise}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{notation}[theorem]{Notation}
\newtheorem{problem}[theorem]{Problem}
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{remark}[theorem]{Remark}
\newtheorem{solution}[theorem]{Solution}
\newtheorem{summary}[theorem]{Summary}
\newenvironment{proof}[1][Proof]{\noindent\textbf{#1.} }{\ \rule{0.5em}{0.5em}}
\begin{document}
El dominio de la funci\'{o}n $f(x)=\sqrt{x^{2}-7}+\dfrac{1}{x-2}\medskip
$\newline\qquad a) $\left\{  x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\mid\left\vert x\right\vert \geq\sqrt{7}\right\}  \qquad\qquad$b) $\left\{
x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\mid x\geq\sqrt{7}\right\}  \medskip$\newline\qquad c) $\left\{  x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\mid x\neq2\right\}  \qquad\qquad\qquad$d) $\left\{  x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\mid x>\sqrt{7}\right\}  $

El dominio de la funci\'{o}n $f(x)=\sqrt{x^{2}-8}+\dfrac{1}{x-3}\medskip
$\newline\qquad a) $\{x\in%
%TCIMACRO{\U{211d} }%
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\mathbb{R}
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\mid\left\vert x\right\vert \geq\sqrt{8}.x\neq3\}\qquad$b) $\left\{  x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\mid x\geq\sqrt{8}\right\}  \medskip$\newline\qquad c) $\left\{  x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\mid x\neq3\right\}  \qquad\qquad\qquad$d) $\left\{  x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\mid x>\sqrt{8}\right\}  $

El dominio de la funci\'{o}n $f(x)=\sqrt{x^{2}-4}+\dfrac{1}{x-4}\medskip
$\newline\qquad a) $\left\{  x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\mid x\leq-\sqrt{4},x\geq\sqrt{4},x\neq4\right\}  \qquad\qquad$b) $\left\{
x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\mid x\geq\sqrt{4}\right\}  \medskip$\newline\qquad c) $\left\{  x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\mid x\neq4\right\}  \qquad\qquad\qquad\qquad\qquad$d) $\left\{  x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\mid x>\sqrt{4}\right\}  $

El dominio de la funci\'{o}n $f(x)=\sqrt{x^{2}}+\dfrac{1}{x-4}$\medskip
\newline\qquad a) $\left\{  x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\mid x\neq4\right\}  \qquad\qquad$b) $\left\{  x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\mid x\geq\sqrt{4}\right\}  \medskip$\newline\qquad c) $\left\{  x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\mid x\leq4\right\}  \qquad\qquad$d) $\left\{  x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\right\}  $

El dominio de la funci\'{o}n $f(x)=\sqrt{x^{2}-2}+\dfrac{1}{x-4}$%
\medskip\newline\qquad a) $\left\{  x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\mid x\leq-\sqrt{2},\text{ }\sqrt{2}\leq x,\text{ }x\neq4\right\}
\qquad\qquad$b) $\left\{  x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\mid x^{2}\geq2\right\}  \medskip$\newline\qquad c) $\left\{  x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\mid x\neq4\right\}  \qquad\qquad\qquad\qquad$d) $\left\{  x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\mid x>\sqrt{2}\right\}  $

El dominio de la funci\'{o}n $f(x)=\sqrt{3x+5}+\dfrac{1}{x-4}$\medskip
\newline\qquad a) $\left\{  x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\mid x\geq-\frac{5}{3},x\neq4\right\}  $\qquad b) $\left\{  x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\mid x>4\right\}  \medskip$\newline\qquad c) $\left\{  x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\mid x>-\frac{5}{3},x\neq4\right\}  $\qquad d) $\left\{  x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\mid x\neq4\right\}  $

El dominio de la funci\'{o}n $f(x)=\sqrt{2x^{2}-2}+\dfrac{1}{x-3}$
\medskip\newline\qquad a) $\left\{  x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\mid x\neq3\right\}  $\qquad b) $\left\{  x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\mid x>1\right\}  \medskip$\newline\qquad c) $\left\{  x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\mid x\geq1\right\}  $\qquad d) $\left\{  x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\mid x\leq-1,x>1\right\}  $

El dominio de la funci\'{o}n $f(x)=\sqrt{x-4}+\dfrac{1}{x+2}$ \medskip
\newline\qquad a) $\left\{  x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
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\mid x\geq4\right\}  $\qquad b) $\left\{  x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\mid x\neq-2\right\}  \medskip$\newline\qquad c) $\left\{  x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
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\mid x\geq0\right\}  $\qquad d) $\left\{  x\in%
%TCIMACRO{\U{211d} }%
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\mathbb{R}
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\mid x>-2\right\}  $

El dominio de la funci\'{o}n $f(x)=\sqrt{x^{2}-9}+\dfrac{1}{x-3}$%
\medskip\newline\qquad a) $\left\{  x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
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\mid x\neq3\right\}  $\qquad b) $\left\{  x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\mid x\leq-\sqrt{3},x>\sqrt{3}\right\}  \medskip$\newline\qquad c) $\left\{
x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\mid x>3\right\}  $\qquad d) $\left\{  x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\mid x\geq\sqrt{3}\right\}  $

El dominio de la funci\'{o}n $f(x)=\sqrt{x-\frac{1}{4}}+\dfrac{1}%
{3x-1}\medskip$\newline\qquad a) $\left\{  x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
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\mid x\geq\frac{1}{4},x\neq\frac{1}{3}\right\}  $\qquad b) $\left\{  x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\mid x>\frac{1}{3}\right\}  \medskip$\newline\qquad c) $\left\{  x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\mid x\neq\frac{1}{3}\right\}  $\qquad d) $\left\{  x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\mid x\geq\frac{1}{4}\right\}  $

El dominio de la funci\'{o}n $f(x)=\sqrt{x^{2}-5}+\dfrac{1}{5x-4}$%
\medskip\newline\qquad a) $\left\{  x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
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\mid x\neq\frac{4}{5}\right\}  $\qquad b) $\left\{  x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\mid x>\sqrt{5}\right\}  \medskip$\newline\qquad c) $\left\{  x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\mid x>\frac{4}{5}\right\}  $\qquad d) $\left\{  x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\mid x\leq-\sqrt{5},x>\sqrt{5}\right\}  $

El dominio de la funci\'{o}n $f(x)=\sqrt{x-1}+\dfrac{1}{3x-5}$ \medskip
\newline\qquad a) $\left\{  x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\mid x>1,x\neq\frac{5}{3}\right\}  $\qquad b) $\left\{  x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\mid x<\frac{5}{3},x\geq1\right\}  \medskip$\newline\qquad c) $\left\{  x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\mid x\neq\frac{5}{3}\right\}  $\qquad d) $\left\{  x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\mid x>\frac{5}{3}\right\}  $

El dominio de la funci\'{o}n $f(x)=\sqrt{x^{2}-16}+\dfrac{1}{3x-4}$%
\medskip\newline\qquad a) $\left\{  x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\mid x\neq\frac{4}{3}\right\}  $\qquad b) $\left\{  x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\mid x>4\right\}  \medskip$\newline\qquad c) $\left\{  x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\mid x\leq-4,x>4\right\}  $\qquad d) $\left\{  x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\mid x\geq4,x\neq\frac{4}{3}\right\}  $

El dominio de la funci\'{o}n $f(x)=\sqrt{4x^{2}-16}+\dfrac{1}{x-2}$
\medskip\newline\qquad a) $\left\{  x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\mid x\neq2\right\}  $\qquad b) $\left\{  x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\mid x>2\right\}  \medskip$\newline\qquad c) $\left\{  x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\mid x\leq-2,x>2\right\}  $\qquad d) $\left\{  x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\mid x\geq2\right\}  $

El dominio de la funci\'{o}n $f(x)=\sqrt{x-1}+\dfrac{1}{2x-7}$ \medskip
\newline\qquad a) $\left\{  x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\mid x\geq1,x\neq\frac{7}{2}\right\}  $\qquad b) $\left\{  x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\mid x\geq1\right\}  \medskip$\newline\qquad c) $\left\{  x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\mid x\neq\frac{7}{2}\right\}  $\qquad d) $\left\{  x\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\mid x>\frac{7}{2}\right\}  $


\end{document}